Logarithmic query complexity for approximate Nash computation in large games

Paul W. Goldberg; Francisco J.Marmolejo Cossío; Zhiwei Steven Wu

doi:10.1007/978-3-662-53354-3_1

Logarithmic query complexity for approximate Nash computation in large games

Paul W. Goldberg, Francisco J.Marmolejo Cossío, Zhiwei Steven Wu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

We investigate the problem of equilibrium computation for “large” n-player games where each player has two pure strategies. Large games have a Lipschitz-type property that no single player’s utility is greatly affected by any other individual player’s actions. In this paper, we assume that a player can change another player’s payoff by at most 1/n by changing her strategy. We study algorithms having query access to the game’s payoff function, aiming to find ε-Nash equilibria. We seek algorithms that obtain ε as small as possible, in time polynomial in n. Our main result is a randomised algorithm that achieves ε approaching 1/8 in a completely uncoupled setting, where each player observes her own payoff to a query, and adjusts her behaviour independently of other players’ payoffs/actions. O(log n) rounds/queries are required. We also show how to obtain a slight improvement over 1/8, by introducing a small amount of communication between the players.

Original language	English (US)
Title of host publication	Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings
Editors	Martin Gairing, Rahul Savani
Publisher	Springer Verlag
Pages	3-14
Number of pages	12
ISBN (Print)	9783662533536
DOIs	https://doi.org/10.1007/978-3-662-53354-3_1
State	Published - 2016
Externally published	Yes
Event	9th International Symposium on Algorithmic Game Theory, SAGT 2016 - Liverpool, United Kingdom Duration: Sep 19 2016 → Sep 21 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9928 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	9th International Symposium on Algorithmic Game Theory, SAGT 2016
Country/Territory	United Kingdom
City	Liverpool
Period	9/19/16 → 9/21/16

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.

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10.1007/978-3-662-53354-3_1

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Goldberg, P. W., Cossío, F. J. M., & Wu, Z. S. (2016). Logarithmic query complexity for approximate Nash computation in large games. In M. Gairing, & R. Savani (Eds.), Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings (pp. 3-14). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9928 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-662-53354-3_1

Logarithmic query complexity for approximate Nash computation in large games. / Goldberg, Paul W.; Cossío, Francisco J.Marmolejo; Wu, Zhiwei Steven.
Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings. ed. / Martin Gairing; Rahul Savani. Springer Verlag, 2016. p. 3-14 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9928 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Goldberg, PW, Cossío, FJM & Wu, ZS 2016, Logarithmic query complexity for approximate Nash computation in large games. in M Gairing & R Savani (eds), Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9928 LNCS, Springer Verlag, pp. 3-14, 9th International Symposium on Algorithmic Game Theory, SAGT 2016, Liverpool, United Kingdom, 9/19/16. https://doi.org/10.1007/978-3-662-53354-3_1

Goldberg PW, Cossío FJM, Wu ZS. Logarithmic query complexity for approximate Nash computation in large games. In Gairing M, Savani R, editors, Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings. Springer Verlag. 2016. p. 3-14. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-53354-3_1

Goldberg, Paul W. ; Cossío, Francisco J.Marmolejo ; Wu, Zhiwei Steven. / Logarithmic query complexity for approximate Nash computation in large games. Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings. editor / Martin Gairing ; Rahul Savani. Springer Verlag, 2016. pp. 3-14 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AB - We investigate the problem of equilibrium computation for “large” n-player games where each player has two pure strategies. Large games have a Lipschitz-type property that no single player’s utility is greatly affected by any other individual player’s actions. In this paper, we assume that a player can change another player’s payoff by at most 1/n by changing her strategy. We study algorithms having query access to the game’s payoff function, aiming to find ε-Nash equilibria. We seek algorithms that obtain ε as small as possible, in time polynomial in n. Our main result is a randomised algorithm that achieves ε approaching 1/8 in a completely uncoupled setting, where each player observes her own payoff to a query, and adjusts her behaviour independently of other players’ payoffs/actions. O(log n) rounds/queries are required. We also show how to obtain a slight improvement over 1/8, by introducing a small amount of communication between the players.

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Logarithmic query complexity for approximate Nash computation in large games

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